Can a F-22 detect a J-20 beyond visual range? Probably not.
The F/A-22's radar contains 2,000 T/R modules with a power output of 4 Watts each. The total power output of the F/A-22 AN/APG-77 radar is 8,000 Watts or 8 KW.
The maximum theoretical power that may return to the radar receiver after scattering off the J-20's canards is:
8 KW x 1.035 x 10^-17 = 8.28^-13 Watts or 0.000000000000828 Watts.
The extremely tiny 8.28^-13 Watts of radar energy return will most likely be absorbed by the intervening air, water, dust, clouds, soot, etc. This is true, because we know that "the atmosphere is not perfectly transparent at any radio frequency."
Since military equipment specifications are highly classified, I have no choice and have to make reasonable assumptions to gain insights.
Here, I will assume that the F/A-22 AN/APG-77 radar has the same ballpark performance as the EADS DR 174 3D radar. My previous calculation has shown that a 20 KW DR 174 can detect a F-22/J-20 at 13.5 km. Since the F/A-22 AN/APG-77 has only 8 KW, we expect the F-22 to detect an incoming J-20 at roughly 5.4 km (e.g. 13.5 km * (8 KW/20 KW) = 5.4 km).
The bottom line is that the J-20 is a very big deal. It looks like the F-22 will have to engage the J-20 in a dogfight. In this situation, assuming training is roughly equivalent, the side with the greater number of stealth fighters should have a decisive edge.
"3.0 Technology
The F/A-22's AN/APG-77 radar is an active-element, electronically scanned (that is, it does not move) array of around
2000 finger-sized transmitter / receiver modules. Each module weights ca 15g and has a poweroutput of over 4W. The APG-77 is capable of changing the direction, power and shape of the radar beam very rapidly, so it can acquire target data, and in the meantime minimizing the chance that the radar signal is detected or tracked."
"There may be more water in the air after a rainstorm, or near the ocean. .... shows occur when the
air contains many small particles of dust or water. ... protects us by absorbing and scattering harmful radiation from the sun and space. ..."
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The atmosphere is not perfectly transparent at any radio frequency. The figure below shows how the zenith (the direction directly overhead) opacity z varies with frequency during a typical summer night in Green Bank, WV, with a water-vapor column density of 1 cm, 55% cloud cover, and surface air temperature T=288 K=15 C. The total opacity is the sum of several components (Leibe, H. J. 1985, Radio Science, 20, 1069):
(1) The continuum (broadband) opacity of dry air results from viscous damping of the free rotations of nonpolar molecules. It is relatively small (z001) and nearly independent of frequency.
(2) Molecular oxygen (O2) has no permanent electric dipole moment, but it does have rotational transitions that can absorb radio waves because it has a permanent magnetic dipole moment. The atmospheric-pressure-broadened complex of oxygen spectral lines near 60 GHz is quite opaque (z1) and prevents ground-based observations between about 52 GHz and 68 GHz.
(3) Hydrosols are liquid water droplets small enough (radius 01 mm) to remain suspended in clouds. Since they are much smaller than the wavelength even at 120 GHz (25 mm), their emission and absorption can be described by the Rayleigh approximation and their opacity is proportional to −2 or 2.
(4) The strong water-vapor line at 22235 GHz is pressure broadened to 4 GHz width. The so-called "continuum" opacity of water vapor at radio wavelengths is actually the sum of line-wing opacities from much stronger water lines centered on infrared wavelengths. In the plotted frequency range, this continuum opacity is also proportional to 2. Both the line and continuum zenith opacities are directly proportional to the column density of precipitable water vapor (pwv) along the vertical line-of-sight through the atmosphere. The pwv is conventionally expressed as a length (e.g., 1 cm) rather than a true column density (e.g., 1 gm cm−2), but the two are numerically equivalent because the density of water is one in cgs units."